arXiv 0810.41742008-10math.SG

Correlators and Descendants of Subcritical Stein Manifolds

Jian He

备注：: Proofs completely rewritten. Contains all the results of arXiv:1203.4108v2. Includes computation of Bourgeois-Oancea exact sequence

英文摘要：

We determine contact homology algebra of a subcritical Stein-fillable contact manifold whose first Chern class vanishes. We also compute the genus-0 one point correlators and gravitational descendants of compactly supported closed forms of their subcritical Stein fillings. This is a step towards determining the full potential function of the filling as defined in \cite{EliashbergGiventalHofer}. These invariants also give a canonical presentation of the cylindrical contact homology. With respect to this presentation, we determine the degree-2 differential in the Bourgeois--Oancea exact sequence of \cite{Oancea}. As a further application, we proved that if a Kähler manifold $M^{2n}$ admits a subcritical polarization and $c_1$ vanishes in the subcritical complement, then $M$ is uniruled.

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